What draws the Constraint menu completely?
From the code in  startup/bl_ui/properties_constraints.py .
ConstraintsButtonsPanel class has a draw method defined for each constraint type, for example TRACK_TO

class ConstraintButtonsPanel:
    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "constraint"

    # .... 
    def TRACK_TO(self, context, layout, con):
        self.target_template(layout, con)

        row = layout.row()
        row.label(text="To:")
        row.prop(con, "track_axis", expand=True)

        row = layout.row()
        row.prop(con, "up_axis", text="Up")
        row.prop(con, "use_target_z")

        self.space_template(layout, con)

#....
class OBJECT_PT_constraints(ConstraintButtonsPanel, Panel):    


Notice the OBJECT_PT_constraints class inherits the ConstraintButtonsPanel class, giving it all the attributes defined therein. 

ConstraintsButtonsPanel.TRACK_TO is the layout code for a track-to constraint, without this, the line (when con.type == 'TRACK_TO')

getattr(self, con.type)(context, box, con)


will result in the error

AttributeError: 'Constratints' object has no attribute 'TRACK_TO'


A quick fix would be to import the ConstraintsButtonsPanel class and use it in the getattr(...) call, like so

import bpy

from bl_ui.properties_constraint import ConstraintButtonsPanel

class Constratints(bpy.types.Panel):
    bl_label = "Constratints"
    bl_idname = "Constratints"
    bl_space_type = 'VIEW_3D'
    bl_region_type = 'TOOLS'
    bl_category = "Modeling Toolbox"

    @classmethod
    def poll(cls, context):
        return context.object and context.object.data

    def draw(self, context):
        layout = self.layout
  #      con = DATA_PT_constraints(context)
        ob = context.object

        layout = self.layout
        row = layout.row()

        row.operator_menu_enum("object.constraint_add", "type", text="Add Object Constraint")
        for con in ob.constraints:
            box = layout.template_constraint(con)
            if box:
                getattr(ConstraintButtonsPanel, con.type)(ConstraintButtonsPanel, context, box, con)    
                #getattr(self, con.type)(context, box, con)

bpy.utils.register_class(Constratints)